This thesis proposes to predict the sound emitted from low-speed fans and its scattered-field by installation effects related to industrial applications. Both tonal and broadband components of fan noise are investigated. Methods existing in the literature contain assumptions and simplifications in order to deal with fan noise problems in analytical manner, such as consideration of an observer located in the far-field of the source. Firstly, the effect of far-field assumption in the tonal fan noise formulation is addressed. Using artificial blade sources, a comparison between two closed-form analytical solutions and a numerical technique is performed for validation in free-field. Secondly, the scattered field of the tonal fan noise is investigated using numerical and analytical techniques. The acoustic field of a rotor operating in a finite duct is first investigated combining the closed-form analytical formulations with the Boundary Element Method (BEM). Since BEM would be computationally demanding for high frequency applications, analytical scattering techniques are also introduced. Reflection and scattering of sound waves by a large plane are first addressed replacing the plane with an image source. Secondly, an exact analytical solution considering scattering of the tonal fan noise by a rigid corner is derived. Another point addressed in this thesis is the prediction of the broadband noise generated by a low-speed axial fan operating in turbulent stream. Amiet's theory of turbulence-interaction noise for a stationary air foil is considered. One of the key points proposed in this thesis is an extension of Amiet's method, allowing prediction of the acoustic field of the airfoil in its geometrical near-field in a semi-analytical perspective. The extended formulation is compared with Amiet's classical solution and a reference solution obtained with numerical integration involving no geometrical far-field assumption. Experiments are also performed in anechoic chamber using an isolated airfoil located in grid generated turbulence. Another assumption made in Amiet's theory is the consideration of uniform flow impinging onto the airfoil. However this assumption is not valid for most industrial applications. Different methods exist in literature to deal with this problem. A new approach is proposed in order to take the span wise varying flow conditions into account. Including all the improvements, the broadband acoustic responses of a stationary airfoil located in the developing region of a jet and of a low-speed axial fan operating in a turbulent stream are investigated and validated against measurements. Finally, scattering of the sound generated by the considered airfoil and fan by benchmark obstacles is addressed numerically and analytically. Since BEM is not capable to handle statistical source fields directly, an innovative approach obtained by re-formulating the deterministic BEM method is employed. The final model is compared to the numerical, analytical and experimental solutions for validation purposes.

Cette thèse propose de prédire le bruit émis par des ventilateurs à basse vitesse et sa diffraction par des obstacles liés aux contraintes d’installation dans les applications industrielles. Les composantes tonale et à large bande du bruit sont étudiées. Les méthodes existant dans la littérature considèrent des hypothèses et des simplifications afin de traiter le problème du bruit des ventilateurs de façon analytique, comme par exemple l’approximation de champ lointain. Tout d’abord, l’hypothèse de champ lointain dans la formulation du bruit tonal est relaxée. En utilisant des sources artificielles, une comparaison entre deux expressions analytiques et une simulation numérique est effectuée pour la validation en champ libre. Ensuite, la diffraction du bruit tonal est étudiée par des techniques numériques et analytiques. Le champ acoustique d’un rotor fonctionnant dans un conduit fini est d’abord pris comme exemple en combinant les formulations analytiques avec la méthode d’éléments de frontière (BEM). Etant donné que cette dernière serait trop coûteuse en temps de calcul pour des applications haute fréquence, des techniques analytiques pour le problème de diffraction sont également présentées. La réflexion et la diffraction des ondes sonores par une plaque infinie sont d’abord considérées en remplaçant la plaque par une source image. Ensuite, une solution analytique exacte pour la diffraction du bruit tonal par un coin rigide est formulée. Un autre point abordé dans cette thèse est la prévision du bruit à large bande produit par un ventilateur axial à basse vitesse évoluant dans un écoulement turbulent. La théorie d’Amiet pour le bruit d’interaction de turbulence sur un profil fixe est considérée. Nous en proposons dans cette thèse une extension permettant de prédire le bruit du profil dans son champ proche géométrique l’aide d’outils semi-analytiques. La nouvelle formulation est comparée à solution classique d’Amiet et à une solution de référence obtenue par intégration numérique sans hypothèse de champ lointain géométrique. Des expériences sont également menées dans une soufflerie anéchoide où la turbulence est générée en amont du profil par une grille. Une autre hypothèse du modèle d’Amiet concerne l’écoulement uniforme arrivant sur le profil. Cette hypothèse n’est pas vérifiée dans la plupart des applications industrielles. Différentes méthodes existent dans la littérature pour traiter ce problème. Nous proposons une nouvelle approche pour prendre en compte des conditions d’écoulement variables en envergure. En intégrant toutes ces améliorations, la réponse acoustique large bande d’un profil fixe placé dans un jet turbulent et d’un ventilateur axial à basse vitesse placé dans un écoulement turbulent est étudiée et validée par comparaison avec l’expérience. Dans une dernière partie, la diffraction des ondes acoustiques générées par le profil et le ventilateur par des obstacles est déterminée numériquement et analytiquement. Puisque la méthode BEM n’est pas prévue pour résoudre directement le champ d’une source aléatoire, une approche innovante obtenue par la reformulation de la méthode déterministe de BEM est utilisée. Le modèle final est comparé aux solutions numériques, analytiques et expérimentales pour la validation. / This thesis proposes to predict the sound emitted from low-speed fans and its scattered-field by installation effects related to industrial applications. Both tonal and broadband components of fan noise are investigated. Methods existing in the literature contain assumptions and simplifications in order to deal with fan noise problems in analytical manner, such as consideration of an observer located in the far-field of the source. Firstly, the effect of far-field assumption in the tonal fan noise formulation is addressed. Using artificial blade sources, a comparison between two closed-form analytical solutions and a numerical technique is performed for validation in free-field. Secondly, the scattered field of the tonal fan noise is investigated using numerical and analytical techniques. The acoustic field of a rotor operating in a finite duct is first investigated combining the closed-form analytical formulations with the Boundary Element Method (BEM). Since BEM would be computationally demanding for high frequency applications, analytical scattering techniques are also introduced. Reflection and scattering of sound waves by a large plane are first addressed replacing the plane with an image source. Secondly, an exact analytical solution considering scattering of the tonal fan noise by a rigid corner is derived. Another point addressed in this thesis is the prediction of the broadband noise generated by a low-speed axial fan operating in turbulent stream. Amiet’s theory of turbulence-interaction noise for a stationary air foil is considered. One of the key points proposed in this thesis is an extension of Amiet’s method, allowing prediction of the acoustic field of the airfoil in its geometrical near-field in a semi-analytical perspective. The extended formulation is compared with Amiet’s classical solution and a reference solution obtained with numerical integration involving no geometrical far-field assumption. Experiments are also performed in anechoic chamber using an isolated airfoil located in grid generated turbulence. Another assumption made in Amiet’s theory is the consideration of uniform flow impinging onto the airfoil. However this assumption is not valid for most industrial applications. Different methods exist in literature to deal with this problem. A new approach is proposed in order to take the span wise varying flow conditions into account. Including all the improvements, the broadband acoustic responses of a stationary airfoil located in the developing region of a jet and of a low-speed axial fan operating in a turbulent stream are investigated and validated against measurements. Finally, scattering of the sound generated by the considered airfoil and fan by benchmark obstacles is addressed numerically and analytically. Since BEM is not capable to handle statistical source fields directly, an innovative approach obtained by re-formulating the deterministic BEM method is employed. The final model is compared to the numerical, analytical and experimental solutions for validation purposes.